A common method of making cam shafts is by turning and grinding work pieces. Hitherto cam shaft manufacturers have used a lathe wherein radially movable slides carrying a plurality of holders with fixed spatial relationship are independently movable with respect to one another. The holders, each of which is provided with a cutting insert, have been possible to set relative to the slides in a transverse or radial direction with respect to the rotable work piece. The principal disadvantages, however, of these prior art cam shaft tool reside in the necessities for carefully machining of the axial reaction surfaces for each holder and for the lack of axial positioning possibility.